AI 中文总结
该研究针对维数n≥3的渐近锥形流形上余闭p-形式的Hodge拉普拉斯算子，发展广义本征函数与泛函演算，给出散射矩阵的显式描述，其特殊情形可刻画麦克斯韦方程组的电场。
AI 中文摘要
针对维数n≥3的渐近锥形流形上余闭p-形式的Hodge拉普拉斯算子，我们给出散射矩阵的显式描述。我们发展广义本征函数与泛函演算来阐述该结果，这与标量情形所用的傅里叶积分算子不同。从无穷远处的Hodge分解出发，我们构造余闭的广义本征形式，并建立p-形式Hodge拉普拉斯算子的谱表示。维数n=3且p=1的特殊情形刻画了麦克斯韦方程组的电场。
英文摘要
We give an explicit description of the scattering matrix for the Hodge-Laplacian on co-closed p-forms on asymptotically conic manifolds of dimension $n\geq 3$. We develop generalized eigenfunctions and a functional calculus to describe the result, a departure from the Fourier Integral Operators used in the scalar case. Starting from the Hodge decomposition at infinity, we construct generalized eigenforms which are co-closed and establish a spectral representation for the p-form Hodge Laplacian. The special case of dimension 3 for $p=1$ characterises the electric field for Maxwell's equations.
